numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/EIG/dget37.f | 19144B | -rw-r--r-- |
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*> \brief \b DGET37 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGET37( RMAX, LMAX, NINFO, KNT, NIN ) * * .. Scalar Arguments .. * INTEGER KNT, NIN * .. * .. Array Arguments .. * INTEGER LMAX( 3 ), NINFO( 3 ) * DOUBLE PRECISION RMAX( 3 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGET37 tests DTRSNA, a routine for estimating condition numbers of *> eigenvalues and/or right eigenvectors of a matrix. *> *> The test matrices are read from a file with logical unit number NIN. *> \endverbatim * * Arguments: * ========== * *> \param[out] RMAX *> \verbatim *> RMAX is DOUBLE PRECISION array, dimension (3) *> Value of the largest test ratio. *> RMAX(1) = largest ratio comparing different calls to DTRSNA *> RMAX(2) = largest error in reciprocal condition *> numbers taking their conditioning into account *> RMAX(3) = largest error in reciprocal condition *> numbers not taking their conditioning into *> account (may be larger than RMAX(2)) *> \endverbatim *> *> \param[out] LMAX *> \verbatim *> LMAX is INTEGER array, dimension (3) *> LMAX(i) is example number where largest test ratio *> RMAX(i) is achieved. Also: *> If DGEHRD returns INFO nonzero on example i, LMAX(1)=i *> If DHSEQR returns INFO nonzero on example i, LMAX(2)=i *> If DTRSNA returns INFO nonzero on example i, LMAX(3)=i *> \endverbatim *> *> \param[out] NINFO *> \verbatim *> NINFO is INTEGER array, dimension (3) *> NINFO(1) = No. of times DGEHRD returned INFO nonzero *> NINFO(2) = No. of times DHSEQR returned INFO nonzero *> NINFO(3) = No. of times DTRSNA returned INFO nonzero *> \endverbatim *> *> \param[out] KNT *> \verbatim *> KNT is INTEGER *> Total number of examples tested. *> \endverbatim *> *> \param[in] NIN *> \verbatim *> NIN is INTEGER *> Input logical unit number *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_eig * * ===================================================================== SUBROUTINE DGET37( RMAX, LMAX, NINFO, KNT, NIN ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER KNT, NIN * .. * .. Array Arguments .. INTEGER LMAX( 3 ), NINFO( 3 ) DOUBLE PRECISION RMAX( 3 ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) DOUBLE PRECISION EPSIN PARAMETER ( EPSIN = 5.9605D-8 ) INTEGER LDT, LWORK PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) ) * .. * .. Local Scalars .. INTEGER I, ICMP, IFND, INFO, ISCL, J, KMIN, M, N DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TNRM, TOL, TOLIN, V, $ VIMIN, VMAX, VMUL, VRMIN * .. * .. Local Arrays .. LOGICAL SELECT( LDT ) INTEGER IWORK( 2*LDT ), LCMP( 3 ) DOUBLE PRECISION DUM( 1 ), LE( LDT, LDT ), RE( LDT, LDT ), $ S( LDT ), SEP( LDT ), SEPIN( LDT ), $ SEPTMP( LDT ), SIN( LDT ), STMP( LDT ), $ T( LDT, LDT ), TMP( LDT, LDT ), VAL( 3 ), $ WI( LDT ), WIIN( LDT ), WITMP( LDT ), $ WORK( LWORK ), WR( LDT ), WRIN( LDT ), $ WRTMP( LDT ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEHRD, DHSEQR, DLACPY, DSCAL, DTREVC, $ DTRSNA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, SQRT * .. * .. Executable Statements .. * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM * * EPSIN = 2**(-24) = precision to which input data computed * EPS = MAX( EPS, EPSIN ) RMAX( 1 ) = ZERO RMAX( 2 ) = ZERO RMAX( 3 ) = ZERO LMAX( 1 ) = 0 LMAX( 2 ) = 0 LMAX( 3 ) = 0 KNT = 0 NINFO( 1 ) = 0 NINFO( 2 ) = 0 NINFO( 3 ) = 0 * VAL( 1 ) = SQRT( SMLNUM ) VAL( 2 ) = ONE VAL( 3 ) = SQRT( BIGNUM ) * * Read input data until N=0. Assume input eigenvalues are sorted * lexicographically (increasing by real part, then decreasing by * imaginary part) * 10 CONTINUE READ( NIN, FMT = * )N IF( N.EQ.0 ) $ RETURN DO 20 I = 1, N READ( NIN, FMT = * )( TMP( I, J ), J = 1, N ) 20 CONTINUE DO 30 I = 1, N READ( NIN, FMT = * )WRIN( I ), WIIN( I ), SIN( I ), SEPIN( I ) 30 CONTINUE TNRM = DLANGE( 'M', N, N, TMP, LDT, WORK ) * * Begin test * DO 240 ISCL = 1, 3 * * Scale input matrix * KNT = KNT + 1 CALL DLACPY( 'F', N, N, TMP, LDT, T, LDT ) VMUL = VAL( ISCL ) DO 40 I = 1, N CALL DSCAL( N, VMUL, T( 1, I ), 1 ) 40 CONTINUE IF( TNRM.EQ.ZERO ) $ VMUL = ONE * * Compute eigenvalues and eigenvectors * CALL DGEHRD( N, 1, N, T, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N, $ INFO ) IF( INFO.NE.0 ) THEN LMAX( 1 ) = KNT NINFO( 1 ) = NINFO( 1 ) + 1 GO TO 240 END IF DO 60 J = 1, N - 2 DO 50 I = J + 2, N T( I, J ) = ZERO 50 CONTINUE 60 CONTINUE * * Compute Schur form * CALL DHSEQR( 'S', 'N', N, 1, N, T, LDT, WR, WI, DUM, 1, WORK, $ LWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 2 ) = KNT NINFO( 2 ) = NINFO( 2 ) + 1 GO TO 240 END IF * * Compute eigenvectors * CALL DTREVC( 'Both', 'All', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, N, M, WORK, INFO ) * * Compute condition numbers * CALL DTRSNA( 'Both', 'All', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, S, SEP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF * * Sort eigenvalues and condition numbers lexicographically * to compare with inputs * CALL DCOPY( N, WR, 1, WRTMP, 1 ) CALL DCOPY( N, WI, 1, WITMP, 1 ) CALL DCOPY( N, S, 1, STMP, 1 ) CALL DCOPY( N, SEP, 1, SEPTMP, 1 ) CALL DSCAL( N, ONE / VMUL, SEPTMP, 1 ) DO 80 I = 1, N - 1 KMIN = I VRMIN = WRTMP( I ) VIMIN = WITMP( I ) DO 70 J = I + 1, N IF( WRTMP( J ).LT.VRMIN ) THEN KMIN = J VRMIN = WRTMP( J ) VIMIN = WITMP( J ) END IF 70 CONTINUE WRTMP( KMIN ) = WRTMP( I ) WITMP( KMIN ) = WITMP( I ) WRTMP( I ) = VRMIN WITMP( I ) = VIMIN VRMIN = STMP( KMIN ) STMP( KMIN ) = STMP( I ) STMP( I ) = VRMIN VRMIN = SEPTMP( KMIN ) SEPTMP( KMIN ) = SEPTMP( I ) SEPTMP( I ) = VRMIN 80 CONTINUE * * Compare condition numbers for eigenvalues * taking their condition numbers into account * V = MAX( TWO*DBLE( N )*EPS*TNRM, SMLNUM ) IF( TNRM.EQ.ZERO ) $ V = ONE DO 90 I = 1, N IF( V.GT.SEPTMP( I ) ) THEN TOL = ONE ELSE TOL = V / SEPTMP( I ) END IF IF( V.GT.SEPIN( I ) ) THEN TOLIN = ONE ELSE TOLIN = V / SEPIN( I ) END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( SIN( I )-TOLIN ).GT.STMP( I )+TOL ) THEN VMAX = ONE / EPS ELSE IF( SIN( I )-TOLIN.GT.STMP( I )+TOL ) THEN VMAX = ( SIN( I )-TOLIN ) / ( STMP( I )+TOL ) ELSE IF( SIN( I )+TOLIN.LT.EPS*( STMP( I )-TOL ) ) THEN VMAX = ONE / EPS ELSE IF( SIN( I )+TOLIN.LT.STMP( I )-TOL ) THEN VMAX = ( STMP( I )-TOL ) / ( SIN( I )+TOLIN ) ELSE VMAX = ONE END IF IF( VMAX.GT.RMAX( 2 ) ) THEN RMAX( 2 ) = VMAX IF( NINFO( 2 ).EQ.0 ) $ LMAX( 2 ) = KNT END IF 90 CONTINUE * * Compare condition numbers for eigenvectors * taking their condition numbers into account * DO 100 I = 1, N IF( V.GT.SEPTMP( I )*STMP( I ) ) THEN TOL = SEPTMP( I ) ELSE TOL = V / STMP( I ) END IF IF( V.GT.SEPIN( I )*SIN( I ) ) THEN TOLIN = SEPIN( I ) ELSE TOLIN = V / SIN( I ) END IF TOL = MAX( TOL, SMLNUM / EPS ) TOLIN = MAX( TOLIN, SMLNUM / EPS ) IF( EPS*( SEPIN( I )-TOLIN ).GT.SEPTMP( I )+TOL ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I )-TOLIN.GT.SEPTMP( I )+TOL ) THEN VMAX = ( SEPIN( I )-TOLIN ) / ( SEPTMP( I )+TOL ) ELSE IF( SEPIN( I )+TOLIN.LT.EPS*( SEPTMP( I )-TOL ) ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I )+TOLIN.LT.SEPTMP( I )-TOL ) THEN VMAX = ( SEPTMP( I )-TOL ) / ( SEPIN( I )+TOLIN ) ELSE VMAX = ONE END IF IF( VMAX.GT.RMAX( 2 ) ) THEN RMAX( 2 ) = VMAX IF( NINFO( 2 ).EQ.0 ) $ LMAX( 2 ) = KNT END IF 100 CONTINUE * * Compare condition numbers for eigenvalues * without taking their condition numbers into account * DO 110 I = 1, N IF( SIN( I ).LE.DBLE( 2*N )*EPS .AND. STMP( I ).LE. $ DBLE( 2*N )*EPS ) THEN VMAX = ONE ELSE IF( EPS*SIN( I ).GT.STMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SIN( I ).GT.STMP( I ) ) THEN VMAX = SIN( I ) / STMP( I ) ELSE IF( SIN( I ).LT.EPS*STMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SIN( I ).LT.STMP( I ) ) THEN VMAX = STMP( I ) / SIN( I ) ELSE VMAX = ONE END IF IF( VMAX.GT.RMAX( 3 ) ) THEN RMAX( 3 ) = VMAX IF( NINFO( 3 ).EQ.0 ) $ LMAX( 3 ) = KNT END IF 110 CONTINUE * * Compare condition numbers for eigenvectors * without taking their condition numbers into account * DO 120 I = 1, N IF( SEPIN( I ).LE.V .AND. SEPTMP( I ).LE.V ) THEN VMAX = ONE ELSE IF( EPS*SEPIN( I ).GT.SEPTMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I ).GT.SEPTMP( I ) ) THEN VMAX = SEPIN( I ) / SEPTMP( I ) ELSE IF( SEPIN( I ).LT.EPS*SEPTMP( I ) ) THEN VMAX = ONE / EPS ELSE IF( SEPIN( I ).LT.SEPTMP( I ) ) THEN VMAX = SEPTMP( I ) / SEPIN( I ) ELSE VMAX = ONE END IF IF( VMAX.GT.RMAX( 3 ) ) THEN RMAX( 3 ) = VMAX IF( NINFO( 3 ).EQ.0 ) $ LMAX( 3 ) = KNT END IF 120 CONTINUE * * Compute eigenvalue condition numbers only and compare * VMAX = ZERO DUM( 1 ) = -ONE CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Eigcond', 'All', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 130 I = 1, N IF( STMP( I ).NE.S( I ) ) $ VMAX = ONE / EPS IF( SEPTMP( I ).NE.DUM( 1 ) ) $ VMAX = ONE / EPS 130 CONTINUE * * Compute eigenvector condition numbers only and compare * CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Veccond', 'All', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 140 I = 1, N IF( STMP( I ).NE.DUM( 1 ) ) $ VMAX = ONE / EPS IF( SEPTMP( I ).NE.SEP( I ) ) $ VMAX = ONE / EPS 140 CONTINUE * * Compute all condition numbers using SELECT and compare * DO 150 I = 1, N SELECT( I ) = .TRUE. 150 CONTINUE CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Bothcond', 'Some', SELECT, N, T, LDT, LE, LDT, $ RE, LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, $ INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 160 I = 1, N IF( SEPTMP( I ).NE.SEP( I ) ) $ VMAX = ONE / EPS IF( STMP( I ).NE.S( I ) ) $ VMAX = ONE / EPS 160 CONTINUE * * Compute eigenvalue condition numbers using SELECT and compare * CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Eigcond', 'Some', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 170 I = 1, N IF( STMP( I ).NE.S( I ) ) $ VMAX = ONE / EPS IF( SEPTMP( I ).NE.DUM( 1 ) ) $ VMAX = ONE / EPS 170 CONTINUE * * Compute eigenvector condition numbers using SELECT and compare * CALL DCOPY( N, DUM, 0, STMP, 1 ) CALL DCOPY( N, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Veccond', 'Some', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 180 I = 1, N IF( STMP( I ).NE.DUM( 1 ) ) $ VMAX = ONE / EPS IF( SEPTMP( I ).NE.SEP( I ) ) $ VMAX = ONE / EPS 180 CONTINUE IF( VMAX.GT.RMAX( 1 ) ) THEN RMAX( 1 ) = VMAX IF( NINFO( 1 ).EQ.0 ) $ LMAX( 1 ) = KNT END IF * * Select first real and first complex eigenvalue * IF( WI( 1 ).EQ.ZERO ) THEN LCMP( 1 ) = 1 IFND = 0 DO 190 I = 2, N IF( IFND.EQ.1 .OR. WI( I ).EQ.ZERO ) THEN SELECT( I ) = .FALSE. ELSE IFND = 1 LCMP( 2 ) = I LCMP( 3 ) = I + 1 CALL DCOPY( N, RE( 1, I ), 1, RE( 1, 2 ), 1 ) CALL DCOPY( N, RE( 1, I+1 ), 1, RE( 1, 3 ), 1 ) CALL DCOPY( N, LE( 1, I ), 1, LE( 1, 2 ), 1 ) CALL DCOPY( N, LE( 1, I+1 ), 1, LE( 1, 3 ), 1 ) END IF 190 CONTINUE IF( IFND.EQ.0 ) THEN ICMP = 1 ELSE ICMP = 3 END IF ELSE LCMP( 1 ) = 1 LCMP( 2 ) = 2 IFND = 0 DO 200 I = 3, N IF( IFND.EQ.1 .OR. WI( I ).NE.ZERO ) THEN SELECT( I ) = .FALSE. ELSE LCMP( 3 ) = I IFND = 1 CALL DCOPY( N, RE( 1, I ), 1, RE( 1, 3 ), 1 ) CALL DCOPY( N, LE( 1, I ), 1, LE( 1, 3 ), 1 ) END IF 200 CONTINUE IF( IFND.EQ.0 ) THEN ICMP = 2 ELSE ICMP = 3 END IF END IF * * Compute all selected condition numbers * CALL DCOPY( ICMP, DUM, 0, STMP, 1 ) CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Bothcond', 'Some', SELECT, N, T, LDT, LE, LDT, $ RE, LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, $ INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 210 I = 1, ICMP J = LCMP( I ) IF( SEPTMP( I ).NE.SEP( J ) ) $ VMAX = ONE / EPS IF( STMP( I ).NE.S( J ) ) $ VMAX = ONE / EPS 210 CONTINUE * * Compute selected eigenvalue condition numbers * CALL DCOPY( ICMP, DUM, 0, STMP, 1 ) CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Eigcond', 'Some', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 220 I = 1, ICMP J = LCMP( I ) IF( STMP( I ).NE.S( J ) ) $ VMAX = ONE / EPS IF( SEPTMP( I ).NE.DUM( 1 ) ) $ VMAX = ONE / EPS 220 CONTINUE * * Compute selected eigenvector condition numbers * CALL DCOPY( ICMP, DUM, 0, STMP, 1 ) CALL DCOPY( ICMP, DUM, 0, SEPTMP, 1 ) CALL DTRSNA( 'Veccond', 'Some', SELECT, N, T, LDT, LE, LDT, RE, $ LDT, STMP, SEPTMP, N, M, WORK, N, IWORK, INFO ) IF( INFO.NE.0 ) THEN LMAX( 3 ) = KNT NINFO( 3 ) = NINFO( 3 ) + 1 GO TO 240 END IF DO 230 I = 1, ICMP J = LCMP( I ) IF( STMP( I ).NE.DUM( 1 ) ) $ VMAX = ONE / EPS IF( SEPTMP( I ).NE.SEP( J ) ) $ VMAX = ONE / EPS 230 CONTINUE IF( VMAX.GT.RMAX( 1 ) ) THEN RMAX( 1 ) = VMAX IF( NINFO( 1 ).EQ.0 ) $ LMAX( 1 ) = KNT END IF 240 CONTINUE GO TO 10 * * End of DGET37 * END